In current clinical practice, various image processing methods are used to correct and facilitate interpretation of digital X-ray images, including: sharpening, enhancing of anatomical structure imaging, automatic targeting of range of interest etc. Some of the most important methods for X-ray image enhancement include noise suppression methods. Noise suppression ensures better visual perception and distinctiveness of low-contrast details and improves quality of execution of other image processing algorithms. Therefore, one of high priority tasks in modern digital radiology is to develop noise filtering methods, capable of preserving diagnostically relevant information and providing high-speed processing at significant levels of noise, dependent on signal intensity.
One can identify two major problems, faced by a researcher who undertakes to develop a digital X-ray image filtering algorithm. The first problem refers to estimation of image noise level, which essentially depends on signal intensity. The second problem refers to development of a filtering method that would ensure the right balance between filtering quality and filtering speed. A closer look should be taken at each of these problems.
The problem of estimation of noise, dependent on signal intensity, can be summarized as follows. Practically any qualitative method for digital image noise filtering involves use of data on amplitude and spectral distribution of noise. In fairly wide range of noise suppression methods, noise variance value is utilized as a parameter. Publications by various authors often use a model, which addresses to digital image noise as a stationary random process with normal amplitude distribution and spectral distribution of white noise. Also, studies of non-stationary noise suppression problem are underway, to be more specific, with regards to noise with signal-dependent variance, and it has been shown that the more accurate is the known noise variance value, the more effective is the noise suppression process [Bosco et. al., Noise Reduction for Cfa Image Sensors Exploiting Hvs Behavior, Sensors 9(3), 1692-1713, 2009; Foi, Practical Denoising of Clipped or Overexposed Noisy Images, Proc. 16th European Signal Process. Conf., EUSIPCO, 2008].
The nature of digital X-ray image noise should be examined. A detector measures intensity of attenuated (by passing through the object examined) X-ray radiation. During imaging each detector cell accumulates the average of N electrons due to absorption of photons. The quantity of accumulated electrons N can be simulated as a Poisson distributed random variable:
            P      ⁡              (                  N          =          n                )              =                  exp        ⁡                  (                      -                          N              _                                )                    ⁢                          ⁢                                    N            _                    n                          n          !                      ,      n    ≥    0.  
Accidental fluctuations of the number of absorbed photons are called photon noise. In modern detectors, photon noise is the primary source of noise. Additional sources include detector system noises, such as: reading noise, thermal noise, amplifier noise, quantization distortion etc. Cumulative effect of such noises is simulated as a Gaussian distributed random variable [Bosco et. al., Noise Reduction for Cfa Image Sensors Exploiting Hvs Behavior, Sensors 9(3), 1692-1713, 2009; Foi et. al., Practical poissonian-gaussian noise modeling and fitting for single-image raw-data, Image Processing, IEEE Transactions, TIP-03364-2007-FINAL]. According to a widely used model, in linear electronic circuits variance of photon noise and additional noises is linearly dependent on useful signal value [Yane, Digital image processing, Moscow, Technosphera, 2007]σ2(u(p))=au(p)+b,  (1)
where u(p) represents signal intensity level in pixel p=(i, j) of an image, and σ2(u(p)) represents noise variance dependence on signal intensity.
Therefore digital image noise is linearly dependent on signal intensity. There is a considerable number of publications on the problem of estimation of signal-dependent noise [Bosco et. al., Noise Reduction for Cfa Image Sensors Exploiting Hvs Behavior, Sensors 9(3), p. 1692-1713, 2009;
Foi et. al., Practical poissonian-gaussian noise modeling and fitting for single-image raw-data, Image Processing, IEEE TRANSACTIONS, TIP-03364-2007-FINAL.
Förstner, Image Preprocessing for Feature Extraction in Digital Intensity, Color and Range images, In Springer Lecture Notes on Earth Sciences, 1998;
Hensel et. al., Robust and Fast Estimation of Signal-Dependent Noise in Medical X-Ray Image Sequences, Springer, Proceedings BVM 2006, Hamburg, Germany, March 19-21, p. 46-50, 2006;
Liu et. al., Automatic estimation and removal of noise from a single image, IEEE Transactions on Pattern Analysis and Machine Intelligence, p. 1-35, October, 2006;
Salmeri et. al., Signal-dependent Noise Characterization for Mammographic Images Denoising. 16th IMEKO TC4 Symposium (IMEKOTC4 '08), Florence, Italy, 2008;
Waegli, Investigations into the Noise Characteristics of Digitized Aerial Images, In: Int. Arch. For Photogr. And Remote Sensing, Vol. 32-2, 1998]. For example, the following study [Hensel et. al., Robust and Fast Estimation of Signal-Dependent Noise in Medical X-Ray Image Sequences, Springer, 2006] refers to establishing a distribution-free method for frame-by-frame estimation of noise in series of digital X-ray images, specifically emphasizing development of an algorithm, suitable for real-time execution. The study [Foi et. al., Practical poissonian-gaussian noise modeling and fitting for single-image raw-data, Image Processing, IEEE Transactions on 17, 1737-1754, 2008] describes a two-parameter approach to digital image noise estimation. Noise of original digital image (as captured by detector and not yet subjected to non-linear transformations such as gamma correction etc.) is simulated based on a random variable, which represents an additive to the signal:un(p)=u(p)+σ2(u(p))n(p),  (2)
where un(p) represents signal intensity level in pixel p of the noisy image observed, and σ2(u(p)) represents noise variance dependence on intensity of a signal of type (1), and n(p)εN(0,1) represents a standard normal random variable. The above study advances a method for tracing noise variance simulation curves, which takes into account sensor nonlinearities, causing underexposure and overexposure, i.e. delinearity at the edges of dynamic range.
The second problem refers to necessity to achieve balance between filtering quality and high-speed filtering requirement. In modern X-ray units, the necessity for rapid high-resolution image processing is somewhat contradictory to commitment to high filtering quality. By now, there has been developed and put to use an extensive mathematical apparatus, related to digital image noise suppression challenge. In general, virtually any noise suppression method can be assigned to one of two classes of filtering methods:
filtering in image transformation space;
filtering in original image space.
The first group of methods (filtering in transformation space) refers to conversion of an original image by applying some transformation. Such transformation is followed by processing transformation factors based on a certain rule, e.g. by applying an appropriate nonlinear operator. This kind of processing is aimed at reduction of noise energy and, possibly, enhancing image sharpness. The final stage of the filtering process is image reconstruction by inverse transformation. This group includes a wide range of methods based on: Fourier transform, wavelet transform [Strang et. al., Wavelets and Filter Banks, Wellesley-Cambridge Press.; Vetterli et. al., Wavelets and Subband Coding, Prentice Hall, Englewood Cliffs, N.J., 1995], complex wavelet transform [Kingsbury, The dual-tree complex wavelet transform: A new technique for shift invariance and directional filters, In Proc. 8th IEEE DSP Workshop, Utah, Aug. 9-12, 1998, paper no. 86; Selesnick, The double-density dual-tree discrete wavelet transform. IEEE Trans. Signal Processing, vol. 52, no. 5, pp. 1304-1314, May 2004], curvelet transform [Candes et. al., Curvelets, multiresolution representation, and scaling laws, In SPIE conference on Signal and Image Processing: Wavelet Applications in Signal and Image Processing VIII, San Diego, 2000] etc. Execution speed and filtering quality in this class of methods are determined by transformation type and factor processing method used.
The second group of methods (filtering in original image space) includes equally extensive list of approaches, including: anisotropic diffusion [Weickert, Anisotropic Diffusion in Image Processing. Tuebner Stuttgart, 1998], variation based algorithms [Rudin et. al., Nonlinear total variation based noise removal algorithms, Physica D, 60:259-268, 1992], bilateral filtering [Tomasi et. al., Bilateral Filtering for Gray and Color Images, In Proc. 6th Int. Conf Computer Vision, New Delhi, India, 1998, pp. 839-846], non-local means filtering [Buades et. al., On image denoising methods, SIAM Multiscale Modeling and Simulation, 4(2):490-530, 2005], regression filtering [Takeda et. al., Kernel regression for image processing and reconstruction, IEEE Transactions on Image Processing, vol. 16, no. 2, pp. 349-366, February 2007], optimal spatial adaptation filtering [Kervrann et. al., Optimal spatial adaptation for patch-based image denoising. IEEE Transactions on Image Processing, vol. 15, no. 10, October 2006] etc. As a rule, such methods reduce to searching for similarity in pixels or groups of pixels (blocks or patches) within the image itself, possibly based on geometric data (such as local orientation of image structures), and application of some pattern for modification (equalization) of brightness of such pixels, whereby modification rate is dependent on degree of similarity of pixels (pixel blocks).